With a huge amount of help from Norbert Michel of Rheingau Genealogie I now know where the Lochmühle (translates as loch mill or hole mill) of Rauenthal is. A whole generation (and more) of Beringer children were born in the Lochmühle, and so I hoped to find out its location so that one day I might be able to visit, or at least stand outside and ponder that I was standing where my Beringers ancestors had once stood.
In correspondence with Norbert I asked him if he knew where the Lochmühle of Rauenthal was, and whether it still existed. He dug up a book, which contained information about the Lochmühle and its succession of owners. It listed Lorenz and Valentin Behringer (sic) as owners and also noted that Lorenz ran it with Valentin Rudolph. Interestingly, Lorenz's wife's maiden name was Rudolph, though her father was Adam Rudolph. I had wondered why the Beringers had been milling in Niederwalluf but then changed to Rauenthal/Schlangenbad. It appears that it could have been a family connection - perhaps Valentin Rudolph was Lorenz's brother-in-law.
The book also had photos/pictures of the mill, one of it in days gone by, the other in its present state. It turns out that I had already come across a photo of the present day mill, but just didn't know it was the right one. You can see a photo of it here, and an illustration of it in 1900 here. Probably one of the things which threw me off was that it is actually closer to Schlangenbad than Rauenthal, though it is found between the two villages. However, I don't doubt that it is the correct mill because Lorenz Beringer's death record actually lists the location of his death as "auf der Lochmühle bei Schlangenbad" - roughly translated as "at the loch mill near Schlangenbad", whilst Valtin Beringer's children were all born at the Lochmühle in Rauenthal. Knowing that Lorenz and Valtin both owned or were tenants of the same mill clinches it.